Question

Imagine that a friend, a savvy student eager to save money where they can, complains to you about increases in the costof living. Your friend says that the cost of their cell-planhas gone up by 25% since last year, clothes havegone up 25%, groceries have gone up 40%, and gasoline has gone up 15%. Imagine that your friend previously spent $100 per month on each of these things (i.e., $100 on cell phone, $100 on clothes, etc.). She confidently states that these changes amountto a 100% increase in the monthly cost of living. Is your friend correct or incorrect in this claim? Calculate the change in monthly cost of living to support your decision.

Answer 1

Increase in cost of cell phones = 25%

Increase in cost of clothes = 25%

Increase in cost of groceries = 40%

Increase in cost of gasoline = 15%

Initial monthly cost of living = $(100 + 100 + 100 + 100) =$400

Increased monthly cost of living $ ( 100*1.25 + 100*1.25 + 100*1.4 + 100*1.15 = $505

Thus, change in monthly cost of living = (505 - 400)/400 = 0.2625 = 26.25%.

Thus, the claim of friend that there is a100% increase in monthly cost of living is incorrect.